How to select ML model when we have 5 classification output variable

I have data with the outcome variable with 5 different classifications so which ML model is best to use here

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Your statement is bit unclear.

Is there one output variable which has 5 possible values (or) are there 5 output variables?

If its the first case, it’s just an ordinary classification problem. Start with simpler models like logistic regression,Decision Trees,SVM.

It depends of your problem and your data. Generally gradient boosting trees have a good accuracy but they need high cpu and memory performance or you will need to wait much time. Try to make train error almost equal to test error to avoid bias and variance.

Try 2 or 3 model and as per accuracy score you can choose the best model for you data.

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